| Cauchy and Heine Definitions of Limit
One of the most common indeterminate forms found in calculus is 0/0. It's called indeterminate because its value is uncertain and can vary from one limit to another. This particular expressions are obtained when attempting to find the limit of a rational expression. If both the numerator and the denominator of the function are zero, then the limit is indeterminate.
There are many techniques suitable to find indeterminate limits. The most-used and suitable for a great variety of problems is the L'Hopital's Rule (also known as L'Hospital Rule):
Application (single or repeated) of the rule usually converts an indeterminate form to an expression that can be easily evaluated by substitution. L'Hopital's rule states that under certain conditions, and being
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